Multilayered Piezoelectric Structures Research Articles

Microwave Diamond-Based HBAR as a Highly Sensitive Sensor for Multiple Applications: Acoustic Attenuation in the Mo Film.

The application of microwave diamond-based HBAR as a sensor of microwave acoustic attenuation α was considered, using the Mo film as an object of research. A multilayered piezoelectric structure, as the Al/Al0.73Sc0.27N/Mo/(100) diamond/Mo, was produced using aluminum-scandium nitride composition, and was studied in detail for a number of the Mo films with different thicknesses obtained by magnetron deposition. The operational frequency band of 3.3 … 18 GHz was used. It was found that the dependence of the resonant frequency shift vs. the h(Mo) thickness for all the overtones to be investigated was linear. For a given sensor, it was found that the mass sensitivity per unit area rm was equal to -26 × 10-12 and -8.7 × 10-12 g/(cm2∙Hz) at 6.0 GHz and 18.3 GHz, respectively. The frequency dependencies of quality factor Q, which changed as a result of Mo film deposition, were considered as the basic experimental data. A method for extracting the α(Mo) values was proposed. The Q-factor under the complete deposition of Mo film was 936 nm, and dropped moderately to ~25%. Such values were enough for an aim of the given experiment. The α(f) in molybdenum was obtained, and demonstrated a dependence that was close to quadratic, corresponding to the Akhiezer attenuation law.

Peculiarities of the Acoustic Wave Propagation in Diamond-Based Multilayer Piezoelectric Structures as “Me1/(Al,Sc)N/Me2/(100) Diamond/Me3” and “Me1/AlN/Me2/(100) Diamond/Me3” under Metal Thin-Film Deposition

New theoretical and experimental results of microwave acoustic wave propagation in diamond-based multilayer piezoelectric structures (MPS) as “Me1/(Al,Sc)N/Me2/(100) diamond/Me3” and “Me1/AlN/Me2/(100) diamond/Me3” under three metal film depositions, including the change in the quality factor Q as a result of Me3 impact, were obtained. Further development of our earlier studies was motivated by the necessity of creating a sensor model based on the above fifth layered MPS and its in-depth study using the finite element method (FEM). Experimental results on the change in operational checkpoint frequencies and quality factors under the effect of film deposition are in satisfactory accordance with FEM data. The relatively small decrease in the quality factor of diamond-based high overtone bulk acoustic resonator (HBAR) under the metal layer effect observed in a wide microwave band could be qualified as an important result. Changes in operational resonant frequencies vs. film thickness were found to have sufficient distinctions. This fact can be quite explained in terms of the difference between acoustic impedances of diamond and deposited metal films.

Calculation of reflection and transmission coefficients for waves in multilayered piezoelectric structures using the mixed variable method.

The reflection and transmission (R/T) behavior of elastic waves in an anisotropic multilayered piezoelectric structure bounded by two homogeneous half-spaces is studied using the mixed variable method. The mixed variable method, which is based on the mixed energy matrix, takes the displacement vector at one end of the structure and the stress vector at other end of the structure as the basic variables. The wave equation for a homogeneous piezoelectric layer is transformed into a first-order state equation in the Hamiltonian system by introducing a dual vector. The general solution of the state equation can be expressed in terms of the eigenvalues and eigenvectors of the complex Hamiltonian matrix. A mixed energy matrix is applied to establish the relationship between the generalized displacement and stress vectors on the upper and lower interfaces of a layer. By an efficient recursive algorithm, the global mixed energy matrix is formed for an arbitrarily anisotropic multilayered piezoelectric structure. The R/T coefficients of the waves in an anisotropic multilayered piezoelectric structure are derived by the global mixed energy matrix. Numerical examples are provided to show the robustness of the mixed variable method. The effects of the incident angles, wavenumbers, and critical angles on the R/T coefficients are discussed.

An accurate method for guided wave propagation in multilayered anisotropic piezoelectric structures

The purpose of this paper is to extend and generalize the precise integration method (PIM) and the Wittrick–Williams (W–W) algorithm to analyze the dispersion of guided waves in multilayered anisotropic piezoelectric structures. The analysis shows that the W–W algorithm cannot be directly applied to piezoelectric materials. This is due to the fact that a submatrix of the Hamiltonian matrix is not positive definite for piezoelectric materials such that the eigenvalue count of sublayers is not zero when the divided sublayers are sufficiently small. The reason for this issue is explored by a theoretical analysis, and then, a symplectic transformation is introduced to ensure that the W–W algorithm can conveniently be applied to solve wave propagation problems in multilayered anisotropic piezoelectric structures. The present method not only guarantees that the computation is accurate and stable, but also finds all eigenfrequencies without being missed. Three numerical examples are provided to illustrate the performance of the method, and the results obtained by the method are compared with the published results and the results obtained by the semi-analytical finite element method. The effects of boundary conditions, wave propagation direction, thickness ratios and stacking sequences on the dispersion behavior of guided waves are discussed.

Textured multilayered piezoelectric structures for energy conversion

Piezoelectric materials are essential for the conversion between mechanical and electrical energy, for example in ultrasound imaging and vibrational energy harvesting. Here, we are making and exploring the effects of a new design: co-sintered multilayers with texture (grains of a preferential crystallographic direction). The motivation is the combination of increased piezoelectric response in certain crystallographic directions; multilayer structures where thick films rather than bulk materials can allow higher frequency operation and large area; and co-sintering to avoid detrimental effects from gluing layers together. Samples of the lead-free piezoelectric material Li0.06(K0.52Na0.48)0.94Nb0.71Ta0.29O3 with 0.25 mol% Mn (KNNLTM) were made by tape casting and co-sintering. NaNbO3 platelets with (100) orientation which were used as templates to introduce texture, and polymethyl methacrylate (PMMA) was used as a pore forming agent for making porous substrates. The electrical impedances of the co-sintered samples were recorded and analyzed by equivalent electrical circuit modelling. A texture up to 85% in the [100] crystallographic direction was obtained. The samples displayed ferro- and piezoelectricity, with a maximum thickness coupling coefficient (kt = 0.18) between mechanical and electrical energy in the most textured sample. This demonstrates that the introduction of texture in multilayered, co-sintered piezoelectrics shows promise for improving devices for ultrasound imaging or energy harvesting.

Band Structures Analysis of Elastic Waves Propagating along Thickness Direction in Periodically Laminated Piezoelectric Composites

Existing studies on elastic waves in periodically laminated piezoelectric structures mainly concerned the passive band properties, since the electrical boundaries in the considered structures cannot vary. This paper investigates the tuning of band properties of uncoupled primary and shear (P- and S-) waves along the thickness direction by actively varying the electrical field in periodically multilayered piezoelectric structures consisting of orthotropic materials. The alteration of the electrical field is realized in the multilayered unit cell here by either applying or switching four kinds of electrical boundary conditions, including the electric-open, applied electric capacitance, electric-short, and applied feedback voltage, to the constituent piezoelectric layer via the constituent electrode layers covering both its surfaces. First, the state space formalism is introduced to obtain the partial wave solution of any constituent orthotropic layer in the unit cell. Second, the traditional transfer matrix method is adopted to derive the dispersion equation of general, periodically laminated piezoelectric composites with unit cells consisting of an arbitrary number of piezoelectric layers with various boundaries and of elastic layers. Third, numerical examples are provided to verify the proposed analysis method, and to study the influences of electrode thickness as well as four electrical boundaries on the band structures. All the frequency-related dispersion curves are also illustrated by numerical examples to summarize the general dispersion characteristics of uncoupled P- and S-waves in periodically laminated piezoelectric composites. The main finding is that the innovative dispersion characteristic resulting from the negative capacitance may also be achieved via feedback control.

Benchmark exact free vibration solutions for multilayered piezoelectric composite plates

The development of advanced finite element models suitable for analysis of smart structures depends on a comprehensive understanding of the high layerwise inhomogeneity in mechanical and electric properties present in multilayered piezoelectric composite structures. The assessment of advanced models still continues to rely only on a few well-known benchmark three-dimensional (3D) exact solutions provided by pioneer works, namely, in the 1970s by Pagano as well as Srinivas for composite plates and later in the 1990s by Heyliger and Saravanos for piezoelectric composite plates. To overcome the limited number of test cases whose 3D exact solutions have been published, the method introduced by Heyliger to derive the 3D exact solutions has been successfully implemented using symbolic computing. New benchmark 3D exact free vibration solutions are provided for piezoelectric composite plates that complete a previous work with the static solutions. Two multilayered plates using PVDF piezoelectric material are chosen as test cases under three sets of electrical boundary conditions and considering three plate aspect ratios (from thick to thin plate), in a total of 18 test cases. For each case, the frequencies of the first six thickness modes are presented, along with some representative through-thickness mode shapes.

Wave propagation in layered piezoelectric rectangular bar: An extended orthogonal polynomial approach

Wave propagation in multilayered piezoelectric structures has received much attention in past forty years. But the research objects of previous research works are only for semi-infinite structures and one-dimensional structures, i.e., structures with a finite dimension in only one direction, such as horizontally infinite flat plates and axially infinite hollow cylinders. This paper proposes an extension of the orthogonal polynomial series approach to solve the wave propagation problem in a two-dimensional (2-D) piezoelectric structure, namely, a multilayered piezoelectric bar with a rectangular cross-section. Through numerical comparison with the available reference results for a purely elastic multilayered rectangular bar, the validity of the extended polynomial series approach is illustrated. The dispersion curves and electric potential distributions of various multilayered piezoelectric rectangular bars are calculated to reveal their wave propagation characteristics.

Dynamic Characteristics of a Multi-Functional Bridge Bearing with Built-In Piezocomposite Element

A multi-functional bridge bearing with built-in piezocomposite electricity generating element (PCGE) is being developed by our research team to respond to the growing demand of self-powered sensing devices for the monitoring of bridges by harvesting the energy produced by the traffic-induced vibrations. For the intended application, a multilayered piezoelectric PCGE structure composed of layers of piezoceramic, glass/epoxy, and carbon/epoxy, has been developed to improve the durability, output voltage and power of the piezoceramic. The output voltage of this PCGE can be used for real-time traffic monitoring like in bridge-weigh-in-motion systems and can eventually be exploited to generate the electricity needed for the lighting and functioning of other embedded sensors. This paper presents the results of the dynamic loading tests conducted on a prototype of the proposed multi-functional bridge bearing to enhance its design details and verify the accuracy of the measurement. The results show that the bearing provides reliable measurement for traffic monitoring and enable to conceive details for the improvement of the output voltage of the PCGE. Since bridge bearings, as indispensable devices transferring the loads and movements from the deck to the substructure and foundations of the bridge, are continuously subjected to traffic loads, the proposed bridge bearing appears to be a natural and economic solution that can be applied to existing or newly built bridges without modification of the conventional design while providing additional and valuable functions for the maintenance of the structure.

Calculation of surface acoustic waves in a multilayered piezoelectric structure

The propagation properties of the surface acoustic waves (SAWs) in a ZnO—SiO2—Si multilayered piezoelectric structure are calculated by using the recursive asymptotic method. The phase velocities and the electromechanical coupling coefficients for the Rayleigh wave and the Love wave in the different ZnO—SiO2—Si structures are calculated and analyzed. The Love mode wave is found to be predominantly generated since the c-axis of the ZnO film is generally perpendicular to the substrate. In order to prove the calculated results, a Love mode SAW device based on the ZnO—SiO2—Si multilayered structure is fabricated by micromachining, and its frequency responses are detected. The experimental results are found to be mainly consistent with the calculated ones, except for the slightly larger velocities induced by the residual stresses produced in the fabrication process of the films. The deviation of the experimental results from the calculated ones is reduced by thermal annealing.

Dispersion curves of shear horizontal wave surface velocities in multilayer piezoelectric systems

A precise knowledge of the frequency responses, velocity dispersion, and distinct vibration modes in multilayer piezoelectric structures would permit the optimization of new designs for electromechanical sensor, actuator, and surface acoustic wave (SAW) filter devices under broad and narrow band conditions. In this paper, the singular-value decomposition technique, combined with the global matrix method and scaling procedure, are applied for studying the solutions of shear stationary waves in symmetric multilayer composite piezoelectric systems. This approach eliminates numerical instabilities sometimes appearing in the analysis of this type of piezoelectric systems, by using a multiple scaling strategy in the global matrix processing. The dispersion curves of the surface velocities, obtained by application of the proposed approach, have shown the presence of clearly separated odd and even bands in such a type of piezoelectric devices, which is explained by considering the eigenstates of the system. Details of this bands pattern are calculated and analyzed.

Guided wave propagation in multilayered piezoelectric structures

A general formulation of the method of the reverberation-ray matrix (MRRM) based on the state space formalism and plane wave expansion technique is presented for the analysis of guided waves in multilayered piezoelectric structures. Each layer of the structure is made of an arbitrarily anisotropic piezoelectric material. Since the state equation of each layer is derived from the three-dimensional theory of linear piezoelectricity, all wave modes are included in the formulation. Within the framework of the MRRM, the phase relation is properly established by excluding exponentially growing functions, while the scattering relation is also appropriately set up by avoiding matrix inversion operation. Consequently, the present MRRM is unconditionally numerically stable and free from computational limitations to the total number of layers, the thickness of individual layers, and the frequency range. Numerical examples are given to illustrate the good performance of the proposed formulation for the analysis of the dispersion characteristic of waves in layered piezoelectric structures.

Finite Element Technique for the Assessment of 3-1 and 'Super 1-3' Connectivity Piezoelectric Composite Transducers

This paper describes the use of finite element (FE) technique in the assessment of new types of multilayered piezoelectric composite structure using the PZFlex code. The background information leading to model configuration, including materials properties and boundary conditions, is discussed. This is coupled with an experimental program of model corroboration via a number of key stage prototypes to achieve a model-build-test methodology. Initially the 3-1 connectivity plate and multilayered piezoelectric composites are analyzed. Results from FE and experimental assessment indicate that the 3-1 plate devices offer no benefit over the conventional 1-3 connectivity arrangement. A simple, minimally diced, 3-1 connectivity multilayer device is analyzed and is shown to be suitable for the manufacture of wideband and efficient transducers operating in the 10-100 kHz frequency range for high power applications.

Mathematical Optimization of Multilayer Piezoelectric Devices with Nonuniform Layers by Simulated Annealing

Multilayer ultrasonic transducers with layers of uniform design are in common use. It is also possible to devise such transducers in which the layer design is nonuniform. However, this adds many degrees of freedom to the transducer design, and conventional design techniques are inadequate to realize desired behavior or even to assess potential benefits. In this paper, a theoretical investigation of multilayer piezoelectric structures with nonuniform layers is reported. Results are presented from a study using computer code to solve the one-dimensional wave equation. It is first shown how multilayer structures with nonuniform layer thicknesses generate even and odd harmonics in their frequency response, suggesting that frequency response can be controlled by choice of layer thickness. However, this choice is complicated and it is impossible to analyze all possible combinations of layer thicknesses. Hence, use of the stochastic optimization technique of simulated annealing is reported. Two optimized transducer designs illustrate this. The first design maximizes uniformity of the fundamental, second, and third harmonics of pressure output, achieved to approximately +/-3%. The results suggest additional bandwidth can be achieved for practical applications, as the presence of a finite response at the second harmonic frequency avoids the null usually associated with this frequency. This is further illustrated with the second optimized transducer design in the form of a three-layer 1-3 connectivity piezo-composite transducer for underwater operation.

Study for multilayer piezoelectric composite structure as displacement actuator by Moiré interferometry and infrared thermography experiments

Multilayer piezoelectric structures are widely applied as a smart structure in precise apparatus. When the structure is in service, fractures often occur near the internal electrode layers. To analyze this issue, a multilayer piezoceramic structure used as displacement actuator is investigated both experimentally and numerically in this paper. Through Moiré interferometry experiment, the plane displacement distribution of the structure is obtained, which is holistically consistent with and locally more acute than the one obtained from finite element simulation. This displacement field shows there is considerable non-uniform deformation in the structure, which is caused by electric field concentration near the edge of the internal electrode, and consequently induces serious stress concentration there that may finally lead to significant damage or failure of the structure in its working environment. Furthermore, the thermal phenomena in piezoelectric structures were measured experimentally by applying infrared thermography. The thermo-concentration around interface crack and inside internal microdefects may intensify non-uniform stress distribution and make structure more vulnerable in its working environment. Hence it should be taken into account in the investigation of piezoelectric structures henceforth.

Simultaneous Exact Control of Quasi-Electrostatic Piezoelectric Systems in Multilayered Media

We consider two quasi-electrostatic models in a multilayered piezoelectric structure. Both models only differ on the boundary conditions. For each one of them we prove a boundary observability inequality which together with the Hilbert Uniqueness Method introduced by J.L. Lions allow us to drive both systems to rest at time T with the same control function. We require suitable geometric conditions on the region and the interfaces as well as monotonicity assumptions on the coefficients of the model.

Effect of initial stress on the propagation behavior of SH-waves in multilayered piezoelectric composite structures

The propagation behavior of horizontally polarized shear waves (SH-waves) in a periodic multilayered piezoelectric composite structure with initial stress is taken into account. The multilayered piezoelectric composite structure consists of piezoelectric layer bonded perfectly with polymer layer alternately. Solutions of the mechanical displacement and electrical potential function are obtained by solving the coupled electromechanical field equations for the piezoelectric layer and the polymeric layer, respectively. The phase velocity equation of the SH-waves in the periodic multilayered piezoelectric structure is obtained for the case of SH-waves propagation along the direction normal to the layering. Influence of initial stress on the stop band effect and the dispersion relation of the SH-waves are discussed in detail, respectively. One set of piezoelectric layer-polymeric layer combination system is considered, i.e. PZP-5H ceramic layer–polythene layer. It can be seen from our research results that the stop band effect of the SH-waves propagation is dramatically changed with the increase of the magnitude of the absolute value of initial stress. The dispersion relation changes remarkably also, as the magnitude of absolute value of the initial stress is greater than 100 MPa. The results reported in our research work can be used as the benchmark for the investigation of the wave propagation in the piezoelectric coupled structures and are theoretically significant in the design of wave propagation in the piezoelectric coupled structures as well.

The Electromechanical Response of Multilayered Piezoelectric Structures

The constitutive equations of multilayered piezoelectric structures are derived in a new form. In this form, the electromechanical coupling is presented as an additional stiffness matrix. This matrix is a true property of the piezoelectric structure and is independent of specific mechanical boundary conditions that may apply to the structure. A novel model of the electromechanical response of such structures is presented. This model accounts for the three-dimensional (3-D) kinematics of the structure deformation. Solution of example problems using the new model shows excellent agreement with full 3-D finite element simulations. These solutions are also compared to the results of previous two-dimensional (2-D) model approximations presented in literature, and the inaccuracies associated with these previous models are discussed.

Recursive surface impedance matrix methods for ultrasonic wave propagation in piezoelectric multilayers

Two recursive surface impedance methods are described for acoustic wave propagation in multilayered piezoelectric structures. Both methods have the advantage of conceptual simplicity and flexibility brought about by the transfer matrix method. Moreover they do not have a priori computational limitations with respect to the total number of layers of the stratified structure nor with respect to the thickness of individual layers; nor is the computational stability limited by the frequency range. For both methods, numerical simulations were carried out in order to illustrate their performances and robustness when combined with suitable recursive numerical algorithms.

Static responses of a multilayered anisotropic piezoelectric structure to point force andpoint charge**Publication of the National Institute of Standards and Technology, an agency of the USGovt; not subject to copyright.

This paper studies three-dimensional (3D) static responses of a multilayered anisotropicpiezoelectric structure due to a point force and point charge. The materials in each layerare homogeneous, generally anisotropic, and linearly piezoelectric, and in general differentfrom one another. The interfaces between adjacent layers are perfectly bonded. Thegeneralized Stroh formalism and two-dimensional (2D) Fourier transforms areemployed to find the responses in terms of a 2D integral. For a layered structuremade of ten alternating layers of piezoelectric AlN and InN on an InN substrate,we show that the responses due to the point force and point charge are greatlyinfluenced by the material layering, showing complicated patterns through the layerthickness. Furthermore, the responses exhibit the asymptotic behavior in the case ofhomogeneous infinite space/half-space in a very short distance to the point source, aboutone tenth of the layer thickness. The complicated responses due to the layeredheterogeneity dictate the need for a general 3D analysis in the design of such smartstructures.